New solitary waves, bifurcation and chaotic patterns of Coupled Nonlinear Schrodinger System arising in fibre optics

This study focuses on analyzing a coupled space-time fractional nonlinear Schrodinger equation, which has applications in describing non-relativistic quantum mechanical behavior. The investigation covers various aspects, including the examination of dynamical behaviors and the exploration of optical soliton solutions. The modified F-expansion method is employed to derive these soliton solutions. To visualize and interpret the physical characteristics of the solutions, they are plotted in 2D, 3D, and density plots with appropriate parameter settings. The dynamical behaviors of the equation are discussed by investigating bifurcations at equilibrium points, and the chaotic behavior of the perturbed dynamical system is demonstrated using chaos theory. Phase portraits illustrating bifurcation and chaotic patterns are generated using the RK4 algorithm in Matlab. These findings provide a dynamic and powerful mathematical tool to address a range of nonlinear wave phenomena. Key discoveries include the identification of new solitary wave forms, as well as bifurcation and chaotic solutions. These unique and intriguing solutions have theoretical significance in understanding energy transfer and diffusion processes in mathematical models.